Henry Ernest Dudeney/Puzzles and Curious Problems/9 - Pocket-Money/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $9$

"When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash.

I spend just one-half of what I had on my railway ticket, and then bought a penny newspaper.

When I got to the terminus I spent half of what I had left and twopence more on a telegram.

Then I spent half of the remainder on a bus, and gave threepence to that old match-seller outside the club.

Consequently I arrive here with this single penny.

Now, how much did I start out with?"

$3 \shillings 6 \oldpence$

Tompkins ended up with $1 \oldpence$

Before he paid $3 \oldpence$ to the matchseller, he had $4 \oldpence$

Before spending half of what he had on a bus, he had $8 \oldpence$

Before spending $2 \oldpence$ on a telegram he had $10 \oldpence$

Before spending half of what he had left, he had $20 \oldpence$

Before buying a penny newspaper, he had $21 \oldpence$

Before spending half of what he had on a train ticket, he had $42 \oldpence$

That is, he started with $3 \shillings 6 \oldpence$

$\blacksquare$